Business Calculus Syllabus and Study Guide Overview

Course Overview

Introduction to Business Calculus

This course provides a foundational understanding of calculus concepts and their applications in business, economics, and related fields. The curriculum emphasizes both analytic and geometric interpretations, focusing on real-world applications and problem-solving skills.

• Course Type: 100% Online

• Credit Hours: 4

• Duration: 8 weeks (Summer 2026)

• Instructor: Dr. Young H. Kim, Ph.D.

• Textbook: Calculus And Its Applications, Brief Version, 12th Edition (Pearson)

Core Competencies and Learning Outcomes

Key Calculus Topics

Upon completion, students will be able to understand and apply the following calculus concepts:

• Limits and Continuity: Find limits numerically and graphically; determine continuity.

• Differentiation: Compute derivatives, tangent lines, and apply differentiation rules.

• Exponential and Logarithmic Functions: Analyze, graph, and differentiate these functions.

• Applications of Differentiation: Solve optimization, elasticity, and related rate problems.

• Integration: Find antiderivatives, definite and indefinite integrals, and areas under curves.

• Applications of Integration: Calculate consumer/producer surplus, future value, and improper integrals.

• Functions of Several Variables: Evaluate multivariable functions and partial derivatives.

Course Structure and Module Breakdown

Weekly Topics and Assignments

The course is organized into modules, each focusing on specific calculus concepts. Assignments and quizzes are due weekly, with midterm and final exams proctored online.

Week	Topics	Assignments
1	Limits, Continuity, Differentiation (Sections 1.1-1.8)	Homework, Quiz 1, Discussion
2	Exponential & Logarithmic Functions (Sections 2.1-2.6)	Homework, Quiz 2, Discussion
3	Extrema & Graph Sketching (Sections 3.1-3.4)	Homework, Quiz 3, Discussion
4	Applications of Differentiation (Sections 3.5-3.9)	Homework, Quiz 4, Discussion, Midterm Exam
5	Integration Basics (Sections 4.1-4.3)	Homework, Quiz 5, Discussion
6	Integration Techniques (Sections 4.4-4.6)	Homework, Quiz 6, Discussion
7	Applications of Integration (Sections 5.1-5.3)	Homework, Quiz 7, Discussion
8	Functions of Several Variables (Sections 6.1-6.6)	Homework, Quiz 8, Discussion, Final Exam

Major Topics and Subtopics

Limits and Continuity

Limits are fundamental to calculus, describing the behavior of functions as inputs approach specific values. Continuity ensures a function has no breaks or jumps.

• Definition of Limit: The value a function approaches as the input approaches a point.

• Numerical and Graphical Methods: Estimating limits using tables and graphs.

• Continuity: A function is continuous at a point if the limit exists and equals the function value.

Example: For $f(x) = x^2$, $\lim_{x \to 2} f(x) = 4$.

Differentiation

Differentiation measures how a function changes as its input changes. It is used to find slopes, rates of change, and optimize functions.

• Derivative Definition: $\frac{d}{dx} f(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$

• Rules: Power Rule, Sum-Difference Rule, Product Rule, Quotient Rule, Chain Rule

• Higher-Order Derivatives: Second and third derivatives for acceleration and concavity

Example: $\frac{d}{dx} x^3 = 3x^2$

Exponential and Logarithmic Functions

These functions model growth and decay in business and economics. The natural base $e$ is commonly used.

• Exponential Function: $f(x) = e^x$

• Logarithmic Function: $f(x) = \ln(x)$

• Derivative of $e^x$: $\frac{d}{dx} e^x = e^x$

• Derivative of $\ln(x)$: $\frac{d}{dx} \ln(x) = \frac{1}{x}$

Example: Exponential growth: $\frac{dp}{dt} = kp$

Applications of Differentiation

Calculus is used to solve optimization problems, analyze elasticity, and determine rates of change in business contexts.

• Optimization: Finding maximum and minimum values using derivatives

• Elasticity of Demand: $E(p) = -\frac{p}{q} \frac{dq}{dp}$

• Related Rates: Solving problems where multiple variables change over time

Example: Maximizing revenue: $R(x) = p(x) \cdot x$

Integration

Integration is the reverse process of differentiation, used to find areas, accumulated values, and solve real-world problems.

• Antiderivative: $\int f(x) dx$

• Definite Integral: $\int_a^b f(x) dx$

• Area Under Curve: Calculating total value or cost

Example: $\int_0^2 x dx = 2$

Applications of Integration

Integration is used to compute consumer and producer surplus, future values, and improper integrals.

• Consumer Surplus: Area between demand curve and price

• Future Value: $FV = \int_0^T R(t) e^{r(T-t)} dt$

• Improper Integrals: Evaluating integrals with infinite limits or discontinuities

Example: $\int_1^\infty \frac{1}{x^2} dx$ converges to 1.

Functions of Several Variables

Multivariable calculus extends concepts to functions with more than one input, useful in business for modeling systems.

• Partial Derivatives: $\frac{\partial f}{\partial x}$, $\frac{\partial f}{\partial y}$

• Double Integrals: $\int \int_D f(x, y) dx dy$

• Optimization: Finding extrema for functions of two variables

Example: $f(x, y) = x^2 + y^2$, $\frac{\partial f}{\partial x} = 2x$

Assessment and Grading

Evaluation Methods

• Quizzes: Weekly, via MyLabMath

• Homework: Weekly, via MyLabMath

• Midterm Exam: Online, proctored

• Final Exam: Online, proctored

• Discussion: Weekly participation

Assignment Type	Points
Quizzes	100
Assignments/Projects	100
Mid-term Exam	100
Final Exam	100
Syllabus Quiz & Discussions	10 (extra)

Final Grade	Final Average (%)
A	90 and above
B	80 - 89
C	70 - 79
D	60 - 69
F	Below 60

Summary Table: Major Calculus Topics

Main Topic	Key Concepts	Applications
Limits & Continuity	Limits, Continuity, Graphical/Numerical Methods	Function behavior, business modeling
Differentiation	Derivative, Rules, Tangent Lines	Optimization, rates of change
Exponential & Logarithmic Functions	e, ln, Growth/Decay Models	Finance, population, economics
Applications of Differentiation	Extrema, Elasticity, Related Rates	Business optimization, demand analysis
Integration	Antiderivatives, Definite/Indefinite Integrals	Area, accumulated value
Applications of Integration	Consumer/Producer Surplus, Future Value	Economic analysis, finance
Functions of Several Variables	Partial Derivatives, Double Integrals	Multivariable optimization, modeling

Additional Info

• All assignments and exams are completed online via MyLabMath and Canvas.

• Students are expected to participate regularly and adhere to deadlines.

• Proctored exams require a webcam and may incur a proctoring fee.

• Technical and privacy policies are in place to protect student data and ensure academic integrity.